Exact Arithmetic of Zero and Infinity Based on the Conventional Division by Zero 0/0 = 1

The chief object of this work is to create an exact and consistent arithmetic of zero, denoted 0, and infinity (zero divisor), written as 1/0 and denoted ∞ , based on the conventional division by zero $$ \dfrac{{0}}{{0}}=1. $$ Manifold and undeniable applications of this arithmetic are given in this work in order to show its usefulness.